Bogoliubov coefficients for the twist operator in the D1D5 CFT

Abstract

The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the 'continuum limit'. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation.

arXiv comment51 pages, 2 figures

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• Effect of the deformation operator in the D1D5 CFT
• Lifting of D1-D5-P states
• AdS${}_3$ Holography at Dimension Two
• Lifting at higher levels in the D1D5 CFT
• Analyzing the squeezed state generated by a twist deformation
• Operator mixing in deformed D1D5 CFT and the OPE on the cover
• Full action of two deformation operators in the D1D5 CFT
• Lifting of level-1 states in the D1D5 CFT
• The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$
• Two Kissing Bolts
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• One-Loop Transition Amplitudes in the D1D5 CFT
• Toroidal Tidal Effects in Microstate Geometries
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• Thermalization in the D1D5 CFT
• A model with no firewall
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• Bosonization, cocycles, and the D1-D5 CFT on the covering surface
• Dynamical evolution in the D1D5 CFT
• Bootstrapping the effect of the twist operator in symmetric orbifold CFTs
• The Dual of a Tidal Force in the D1D5 CFT
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• Second order effect of twist deformation in the D1D5 CFT
• AdS3 Holography for 1/4 and 1/8 BPS geometries
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure